$T=2\pi \sqrt{\frac{m(\sqrt a +b)}{ck}}$

If the time period of SHM of rectangular block can be represented asFind the value of $a+b+c$.

**Details and Assumptions**:

Treat the pulley as a disc.

The block and pulley are oscillating in the same phase with the same frequency.

Pulley has sufficient friction for

*Pure Rolling*and mass=m & strings are light and inextensible.Gravity is present.

Zig-zag lines in fig represents spring of spring constant $k$ and $2k$ as shown.

a is a square-free integer and the fraction is in simplest form.